# Simplifying Fractions

*To simplify a fraction, divide the top and bottom by the highest number that*

* can divide into both numbers exactly.*

## Simplifying Fractions

Simplifying (or *reducing*) fractions means to make the fraction as simple as possible.

## How do I Simplify a Fraction ?

There are two ways to simplify a fraction:

## Method 1

Try to **evenly divide** (only whole number answers) both the top and bottom of the fraction by 2, 3, 5, 7 . etc, until we can’t go any further.

### Example: Simplify the fraction *24* **108** :

That is as far as we can go. The fraction simplifies to *2* **9**

### Example: Simplify the fraction *10* **35** :

Dividing by **2** doesn’t work because **35 can’t be evenly divided by 2** (35/2 = 17 )

No need to check **4** (we checked 2 already, and 4 is just 2 2).

But **5** does work!

That is as far as we can go. The fraction simplifies to *2* **7**

Notice that after checking 2 we didn’t need to check 4 (4 is 2 2)?

We also don’t need to check 6 when we have checked 2 and 3 (6 is 2×3).

In fact, when checking from smallest to largest we use prime numbers:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, .

## Method 2

Divide both the top and bottom of the fraction by the Greatest Common Factor (you have to work it out first!).

### Example: Simplify the fraction *8***12** :

The largest number that goes exactly into both 8 and 12 is 4, so *the Greatest Common Factor is 4*.